Two taps together can fill a tank completely in 3 13 minutes. The smal

1.	Two taps together can fill a tank completely in 3 13 minutes. The smallertap takes 3 minutes more than the bigger tap to fill the tank. Howmuch time does each tap take to fill the tank completely ?P.T.O
Answer» Let the volume of the cistern be V. Together two pipes take 3 1/13 mins = 40/13 Rate of both the pipes together = V/(40/13) Let pipes be A and B, Time taken by A = t mins , So rate = V/t Time taken by B = t+3 mins, So rate = V/(t+3) Combined rate = V/t + V/(t+3) We already know that combined rate = V/(40/13) Equating both , V/t + V/(t+3) = V/(40/13) 1/t + 1/(t+3) = 13/40 (t+3+t) / t(t+3) = 13/40 (2t + 3)/ (t^2+3t) = 13/40 80t + 120 = 13t^2 + 39t 13t^2 - 41t - 120 = 0 The quadratic equation yields two roots : 5 and -1.846 , since time cannot be negative Time taken by pipe A = 5 mins Time taken by pipe B = 5+3 = 8 mins Like my answer if you find it useful!

Two taps together can fill a tank completely in 3 13 minutes. The smallertap takes 3 minutes more than the bigger tap to fill the tank. Howmuch time does each tap take to fill the tank completely ?P.T.O

Answer»

Let the volume of the cistern be V.

Together two pipes take 3 1/13 mins = 40/13

Rate of both the pipes together = V/(40/13)

Let pipes be A and B,

Time taken by A = t mins , So rate = V/t

Time taken by B = t+3 mins, So rate = V/(t+3)

Combined rate = V/t + V/(t+3)

We already know that combined rate = V/(40/13)

Equating both ,

V/t + V/(t+3) = V/(40/13)

1/t + 1/(t+3) = 13/40

(t+3+t) / t(t+3) = 13/40

(2t + 3)/ (t^2+3t) = 13/40

80t + 120 = 13t^2 + 39t

13t^2 - 41t - 120 = 0

The quadratic equation yields two roots :

5 and -1.846 , since time cannot be negative

Time taken by pipe A = 5 mins

Time taken by pipe B = 5+3 = 8 mins

Like my answer if you find it useful!